Algebraic groups and their birational invariants

著者

書誌事項

Algebraic groups and their birational invariants

V.E. Voskresenskiĭ ; [translated from the original Russian manuscript by Boris Kunyavski]

（Translations of mathematical monographs, v. 179）

American Mathematical Society, c1998

  • : AMS soft cover

タイトル別名

Algebraicheskie gruppy i ikh birat︠s︡ionalʹnye invarianty

Алгебраические группы и их бирациональные инварианты

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注記

Rev. ed. of: Algebraicheskie tory. 1977

Includes bibliographical references (p. 211-218)

内容説明・目次

巻冊次

ISBN 9780821809051

内容説明

Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book - which can be viewed as a significant revision of the author's book, "Algebraic Tori" (Nauka, Moscow, 1977) - studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

目次

Forms and Galois cohomology Birational geometry of algebraic tori Invariants of finite transformation groups Arithmetic of linear algebraic groups Tamagawa numbers $R$-equivalence in algebraic groups Index formulas in arithmetic of algebraic tori Bibliographical remarks References.
巻冊次

: AMS soft cover ISBN 9780821872888

内容説明

Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

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